Abstract

For free propagation from a focus the Hermite-Gauss wave functions of optics spread in space. In quantum mechanics the Hermite-Gauss functions are referred to as the harmonic oscillator eigen- functions. These functions are used here to describe the interference of wave packets. It has been shown that when transformed to a frame moving with the normal to the wave front trajectories, the Hermite-Gauss functions are constant up to a phase factor which is the Gouy phase. The Gouy phase itself assumes the role of proper space or time coordinate. Along the whole of such a trajectory, the space wave function is proportional to the wave number function. An arbitrary normalisable wave packet can be expanded using the Hermite-Gauss functions as a basis. As example, it is shown that in the co-moving frame, a displaced Gaussian does not spread but rather becomes a coherent state. This allows a particularly simple representation of the Young's interference pattern from two or more slits.